What ports need to be open for TortoiseSVN to authenticate (clear text) and commit?

What's the first part of your Subversion repository URL?

• If your URL looks like: http://subversion/repos/, then you're probably going over Port 80.
• If your URL looks like: https://subversion/repos/, then you're probably going over Port 443.
• If your URL looks like: svn://subversion/, then you're probably going over Port 3690.
• If your URL looks like: svn+ssh://subversion/repos/, then you're probably going over Port 22.
• If your URL contains a port number like: http://subversion/repos:8080, then you're using that port.

I can't guarantee the first four since it's possible to reconfigure everything to use different ports, of if you go through a proxy of some sort.

If you're using a VPN, you may have to configure your VPN client to reroute these to their correct ports. A lot of places don't configure their correctly VPNs to do this type of proxying. It's either because they have some sort of anal-retentive IT person who's being overly security conscious, or because they simply don't know any better. Even worse, they'll give you a client where this stuff can't be reconfigured.

The only way around that is to log into a local machine over the VPN, and then do everything from that system.